The Hardy–Littlewood–Sobolev inequality for a Riesz potentials [1]} shows that for \(1<p<n\)  and \(p^\ast =\frac{np}{n- p}<+\infty \)  there exists a constant \(A_p\)  such that
\(\Vert \mathcal {I}_1 f(x)\Vert _{p^\ast }\le A_p\Vert f\Vert _p,\) 
